UC-NRLF 


EXCHANGE 


The  Conductivity,  Temperature  Coefficients 
of  Conductivity,  and  Dissociation  of  Cer- 
tain Electrolytes  in  Aqueous  Solution 
from  0°  to  35°.    Probable  Induc- 
tive Action  in  Solution,  and 
Evidence  for  the  Com- 
plexity of  the  Ion* 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 


LULA  GAINES  WINSTON, 

BALTIMORE 
June,  3911 


EASTON,  PA.: 

ESCHBNBACH  PRINTING  Co. 

1911 


The  Conductivity,  Temperature  Coefficients 
of  Conductivity,  and  Dissociation  of  Cer- 
tain Electrolytes  in  Aqueous  Solution 
from  0°  to  35°.    Probable  Induc- 
tive Action  in  Solution,  and 
Evidence  for  the  Com- 
plexity of  the  Ion. 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 

LULA  GAINES  WINSTON 

\  \ 


BALTIMORE 
June,   1911 


EASTON,  PA.: 

PRINTING  Co. 
1911 


CONTENTS. 


Page. 

Introduction 5 

Historical 5 

Experimental 12 

Solutions 12 

Water 12 

Discussion  of  Results 13 

Ammonium  Nitrate 14 

Ammonium  Sulphate 15 

Acid  Ammonium  Sulphate 15 

Sodium  Sulphate 16 

Borax 17 

Potassium  Acetate 18 

Potassium  Permanganate 18 

Di-Potassium  Phosphate 19 

Strontium  Acetate 21 

Magnesium  Bromide 22 

Magnesium  Nitrate 22 

Magnesium  Formate 23 

Magnesium  Acetate 24 

Cadmium  Chloride 25 

Cadmium  Bromide 26 

Cadmium  Iodide 27 

Lead  Chloride 28 

Aluminium  Chloride 29 

Aluminium  Nitrate 30 

Aluminium  Sulphate 31 

Chromium  Chloride 31 

Chromium  Sulphate 32 

Manganous  Sulphate 34 

Silver  Nitrate 35 

Cobalt  Bromide 35 

Copper  Sulphate 36 

Uranyl  Chloride 38 

Uranyl  Nitrate 39 

Uranyl  Sulphate 39 

Uranyl  Acetate 40 

Figures 41 

Summary 48 

Biography 50 


251837 


ACKNOWLEDGMENT. 

The  author  wishes  to  take  this  opportunity  to  express  her 
gratitude  to  President  Remsen,  Professors  Morse,  Jones ,  and 
Renouf ,  Associate  Professor  Acree,  and  Dr.  Reid  for  valuable 
instruction  and  advice. 

Special  thanks  are  due  Professor  Jones,  at  whose  suggestion 
and  tinder  whose  guidance  this  investigation  was  carried  out. 

The  author  would  also  gratefully  acknowledge  assistance 
received  from  Professors  Ames  and  Whitehead,  of  the  Depart- 
ment of  Physics. 


The  Conductivity,  Temperature  Coefficients  of  Con- 
ductivity and  Dissociation  of  Certain  Electro- 
lytes in  Aqueous  Solution  from  0°  to  35°* 
Probable  Inductive  Action  in  Solu- 
tion, and  Evidence  for  the 
Complexity  of  the  Ion* 

INTRODUCTION 

This  paper  forms  one  of  a  series  dealing  with  the  conduc- 
tivity of  electrolytes  in  aqueous  solution.  In  it  we  shall  take 
up  for  consideration  the  conductivity,  temperature  coefficients 
of  conductivity,  and  percentage  dissociation  of  certain  salts, 
and  shall  show  how  these  results  confirm  those  already  ob- 
tained, and  point  out  some  new  relations.  The  work  is  part 
of  an  investigation  which  has  been  carried  on  in  this  labora- 
tory for  a  dozen  years  or  more.  The  importance  of  such  an 
investigation  is  obvious,  since  chemistry  is  a  branch  of  the 
science  of  solutions,  and  one  of  the  very  best  methods  of  study- 
ing solutions  is  the  conductivity  method. 

HISTORICAL 

Electrochemical  theories  were  advanced  as  early  as  1807 
by  Davy  and  by  Berzelius.  Berzelius  was  among  the  first 
to  call  attention  to  the  electrically  charged  atom.  Faraday 
appeared  later,  giving  to  the  world  the  laws  which  bear  his 
name.  His  work  has  stood  the  test  of  time.  His  law  show- 
ing the  relation  between  the  quantity  of  electricity  and  amount 
of  decomposition  holds  rigidly  to-day,  and  in  the  light  of  the 
electron  theory  takes  on  a  new  meaning.  In  the  years  1853 
to  1859  Hittorf  determined  the  relative  velocities  of  the  ions 
of  many  salts.  He  pointed  out  a  relation  between  chemical 
activity  and  conductivity,  and  also  called  attention  to  the 
analogy  existing  between  solutions  and  gases.  This  latter 
problem  was  taken  up  later  by  Raoult,  Ostwald,  van't  Hoff, 
and  others.  The  laws  of  Raoult,  dealing  with  the  lowering  of 
the  freezing  point  and  vapor  pressure  of  liquids,  and  Ostwald 's 


dilution  law  are  well  known.  Van't  Hoff,  in  1887,  working  on 
osmotic  pressure,  found  certain  solutions  that  behaved  ab- 
normally. Arrhenius,  attempting  to  explain  their  behavior, 
pointed  out  the  fact  that  salts  and  analogous  substances 
break  down  into  ions.  Thus  was  given  to  the  world  the  theory 
of  electrolytic  dissociation.  Its  truth  is  attested  on  every 
hand.  Facts  once  inexplicable  become  wonderfully  clear 
and  lend  confirmation  to  the  theory.  Many  workers  have 
appeared  in  the  field  since  Arrhenius.  The  most  important  of 
these,  perhaps,  is  Sir  J.  J.  Thomson,  whose  brilliant  experi- 
ments have  well-nigh  revolutionized  our  conception  of  matter. 
The  result  of  the  work  already  done  may  be  summarized 
briefly  as  follows:  The  conductivity  of  electrolytes  in  solu- 
tion is  dependent  primarily  on  two  things,  viz.,  the  number 
of  ions  and  their  velocity.  These  two  factors  may  be  affected 
by  various  others.  The  most  important  of  these  is  tempera- 
ture. The  effect  of  rise  in  temperature  is  chiefly  to  increase 
the  velocity  of  the  ions.  The  number  of  ions  would  not  be  greatly 
affected  unless  they  were  complex.  In  addition  to  the  effect 
of  temperature  on  the  number  and  velocity  of  ions  in  solu- 
tion, there  are  still  other  factors  which,  for  convenience,  may 
be  divided  into  three  classes : 

1 .  Those  dependent  upon  the  solute. 

2.  Those  dependent  upon  the  solvent. 

3.  Those  dependent  upon  the  combination  of  the  solvent 
with  the  solute. 

In  class  i — factors  dependent  upon  the  solute — mention 
should  be  made  first  of  all  of  the  effect  of  valence.  This  would 
determine  largely  the  number  of  ions  capable  of  entering  into 
solution.  As  is  well  known,  the  conductivities  of  binary, 
ternary  and  quaternary  compounds  are  found  to  vary  con- 
siderably. Factors  affecting  the  velocity  of  the  ion  would 
be  the  atomic  weights  and  atomic  volumes  of  the  elements  ex- 
isting in  the  compound.  We  would  naturally  expect  that  the 
velocity  would  be  an  inverse  function  of  the  atomic  weight 
and  atomic  volume.  Experimentally,  however,  this  has  not 
been  found  to  be  true.  Jones  and  Pearce1  found  that  those 

1  Am.  Chem.  J.,  38,  737  (1907). 


elements  which  have  the  smallest  atomic  volumes  have  the 
greatest  hydrating  power.  This  would  tend  to  diminish 
their  velocity. 

As  to  the  factors  dependent  upon  the  solvent,  the  most  im- 
portant are  its  viscosity,  its  dielectric  constant  and  its  asso- 
ciation. 

In  class  3  should  be  placed  the  concentration  of  the  solu- 
tion and  the  power  of  the  solute  and  solvent  to  form  solvates 
with  one  another. 

The  conductivity  of  solutions  has  been  studied  from  each  of 
these  standpoints,  and  much  valuable  data  have  been  ac- 
cumulated. 

The  effect  of  temperature  has  been  worked  out  carefully 
by  Jones  and  his  coworkers,  West,1  Jacobson,2  Clover,3  West,4 
White,5  Wightman,8  and  Hosford.7  Conductivity  always 
increases  with  rise  in  temperature  from  o°  to  65°,  while  dis- 
sociation usually  decreases  slightly.  The  decrease  in  disso- 
ciation would  tend  to  diminish  the  number  of  ions,  and  thus  to 
lessen  the  conductivity,  but  this  effect  is  more  than  offset 
by  the  increased  velocity  of  the  ions  due  to  rise  in  tempera- 
ture. This  decrease  in  dissociation  may  be  accounted  for  in 
two  ways.  It  may  be  due  to  a  decrease  in  the  association  of 
the  solvent,  which  would  tend  to  decrease  the  dissociation  of 
the  dissolved  substance;  or  it  may  be  due  to  the  fact  that  a 
rise  in  temperature  diminishes  the  dielectric  constant  of  the 
solvent  and  consequently  its  dissociating  power,  since,  accord- 
ing to  the  Thompson-Nernst  hypothesis,  a  substance  having 
a  high  dielectric  constant  has  great  dissociating  power.  While, 
as  just  shown,  the  effect  of  temperature  is  to  diminish  the 
number  of  ions  present,  its  effect  on  the  velocity  of  ions  is 
just  the  reverse.  Rise  in  temperature  increases  the  velocity 
of  ions  in  two  ways:  First,  it  diminishes  the  viscosity  of  the 
solvent.  Second,  rise  in  temperature  would  decrease  the 

1  Am.  Chem.  J.,  34,  357  (1905). 

2  Ibid.,  40,  355  (1908). 

3  Ibid.,  43,  187  (1910). 
*Ibid.,  44,  508  (1910). 
s/itd.,44,  159  (1910). 
6 /&«*.,  46,  56  (1911). 

7  Ibid.,  46,  240  (1911). 


8 

complexity  of  the  hydrates  formed.  This  also  would  tend 
to  increase  the  velocity  of  the  ions.  At  all  events,  the  de- 
crease in  the  number  of  ions  seems  to  be  more  than  compen- 
sated for  by  the  increase  in  their  velocity,  and  the  general 
effect  of  rise  in  temperature  is,  therefore,  to  increase  the  con- 
ductivity. 

The  most  important  factor  in  its  effect  on  conductivity 
with  rise  in  temperature  is  hydration.  That  the  dissolved 
substance  combines  with  some  of  the  solvent  to  form  solvates 
seems  now  to  be  an  undisputed  fact,  the  existence  of  hydrates 
in  solution  being  shown  by  several  independent  lines  of  evi- 
dence.1 The  close  connection  between  hydration  and  water 
of  crystallization  has  also  been  established  in  this  laboratory. 

Important  relations  between  amount  of  hydration  and 
temperature  coefficients  of  conductivity  have  been  pointed 
out.  Jones  and  his  coworkers,  Bingham,  McMaster,  Rouil- 
ler,2  Veazey,3  Guy,4  Davis,  Reinhart,  Mahin,5  Schmidt,6  and 
Kreider7  have  made  important  observations  on  the  effect  of 
viscosity  on  the  conductivity  of  electrolytes. 

The  work  in  this  laboratory  has  been  extended  to  non- 
aqueous  solutions.  Apparatus  has  been  improved,  the  range 
of  temperature  has  been  extended,  old  sources  of  error  have 
been  eliminated,  and  the  conductivities  of  hundreds  of  com- 
pounds have  been  added  to  those  already  measured. 

The  problem  has  been  undertaken  in  this  laboratory  of 
measuring  the  conductivity  of  all  of  the  more  common  acids, 
bases  and  salts  in  aqueous  solution,  from  o°  to  65°,  and  of 
calculating  the  dissociation  whenever  possible. 

This  work  will  be  pushed  forward  as  rapidly  and  carefully 
as  possible. 

One  fact,  overlooked  thus  far  in  the  consideration  of  the 
conductivity  of  electrolytes,  is  the  probable  inductive  action8 

1  Publication  No.  60  of  the  Carnegie  Institution  of  Washington. 

2  Publication  No.  80  of  the  Carnegie  Institution  of  Washington. 

3  Am.  Chem.  J.,  41,  433  (1909). 
*Ibid.   46,  131  (1911). 


*  Ibid. 


7  Ibid. 
*Ibid. 


41,  433  (1909). 

42,  37  (1909). 
45,  282  (1911). 
45,  547  (1911). 


of  the  ion  on  the  unionized  molecule.  In  the  solution  of  a 
salt  there  is  every  condition  necessary  for  inductive  action. 
There  are  the  charged  ions,  the  neutral  molecules  and  the 
dielectric  or  solvent.  Ordinary  electrical  induction  in  con- 
ductors, as  is  well  known,  takes  place  as  follows:  A  charged 
body  brought  near  to  a  neutral  body,  but  separated  from  it 
by  a  dielectric,  causes  a  separation  of  the  electricity  in  the 
neutral  body,  drawing  the  opposite  kind  nearest  to  itself  and 
repelling  the  like  charge  to  the  side  farthest  from  itself.  If, 
while  the  charged  body  is  still  near,  the  repelled  charge  in  the 
conductor  is  removed  by  contact  with  some  other  body,  on 
the  removal  of  the  charged  body  the  once  neutral  body  would 
be  left  charged  with  the  opposite  kind  of  electricity.  The 
ion,  a  charged  body,  acting  through  the  water  (a  dielectric) 
on  an  unionized  molecule,  would  produce  just  such  an  effect. 
Several  results  may  follow  from  this.  First,  a  positive  ion 
brought  near  to  a  neutral  molecule,  but  separated  from  it  by 
the  nonconducting  water,  would  cause  a  separation  of  the 
electricity  in  the  molecule;  the  negative  will  be  drawn  near 
to  the  ion  and  the  positive  repelled.  Suppose,  for  instance, 
that  the  repelled  charge  is  not  removed,  the  charged  ion 
would  simply  attach  itself  to  the  molecule,  and  as  a  charged 
system  move  through  the  solution.  Moreover,  this  charged 
system  could  play  the  part  of  the  original  ion  and,  acting 
through  the  water,  in  a  similar  way  draw  other  molecules  to 
itself.  There  would  be  a  limit,  of  course,  to  the  number  of 
molecules  which  could  thus  be  attached.  This,  no  doubt, 
would  be  a  function  of  the  valency  of  the  ion. 

If,  on  the  other  hand,  the  repelled  charge  is  removed  and 
the  inducing  ion  then  moves  off,  the  once  neutral  molecule 
would  be  left  charged  with  a  sign  opposite  to  that  on  the  in- 
ducing ion,  and  moving  through  the  solution  would  be  able 
to  attract  other  molecules  or  oppositely  charged  ions  to  itself. 
This,  of  course,  would  give  rise  to  a  great  complexity  of  ions 
and  molecules.  The  velocity  of  the  ions  would  thus  be  greatly 
affected,  because  their  masses  would  be  greatly  increased. 
This  may  in  a  measure  account  for  the  apparent  discrepancy 
between  the  dissociation  as  found  by  the  freezing  point  method 


10 

and  that  found  by  conductivity,  since  by  this  inductive  ac- 
tion there  would  be  brought  about  a  change  in  the  number  of 
particles  which  would  probably  affect  the  dissociation  as 
found  by  the  freezing  point  method. 

The  effect  on  conductivity,  on  the  other  hand,  would  be 
due  rather  to  a  change  in  the  velocity  of  the  ions.  The  com- 
plex ions  would  tend  to  move  more  slowly  than  the  individual 
ion,  thus  making  the  conductivity  measurements  of  dissocia- 
tion too  low.  The  change  in  the  number  of  particles  would 
not  be  so  apparent  in  the  case  of  conductivity  because,  when, 
by  means  of  induction,  an  ion  attaches  itself  to  a  neutral 
molecule,  it  would  still  give  rise  to  a  charged  system,  and 
would  not  thereby  reduce  the  number  of  charged  particles 
in  solution.  The  breaking  up  of  these  moving  systems  by 
heat  would  show  itself  in  increased  temperature  coefficients. 

Jones  and  Pearce1  have  shown  that  the  dissociation  as 
measured  by  the  conductivity  method  is  less  than  that  cal- 
culated from  the  freezing  point  lowering.  Conditions  were 
chosen  such  that  the  number  of  ions,  velocity  of  ions,  hydra- 
tion  and  viscosity  were  the  same  in  both  cases.  It  was  found 
by  them  that  the  greater  the  dilution,  the  greater  the  differ- 
ence in  dissociation  as  measured  by  the  two  methods.  This 
is  due  to  the  fact  that  the  complexity  of  the  hydrate  is  greater, 
the  greater  the  dilution. 

Evidence  seems  to  be  accumulating  in  many  directions 
that  the  ions  in  solution  are  complex.  Some  interesting  re- 
lations are  brought  out  in  connection  with  the  various  dilu- 
tion laws,  to  which  sufficient  attention  has  not  as  yet  been 
directed,  which  apparently  point  to  the  complexity  of  mole- 
cules in  solution.  Ostwald's  law, 


has  been  found  to  apply  to  weakly  dissociated  electrolytes, 
but  not  at  all  to  strong  electrolytes.  Moreover,  various  dilu- 
tion laws  have  been  formulated  which  apply  to  strong  elec- 
trolytes but  are  extremely  unsatisfactory  when  it  is  attempted 
to  apply  them  to  weaker  electrolytes. 

1  Am.  Chem.  J.,  38,  743  (1907). 


II 


The  question  naturally  arises,  why  this  difference?  The 
thought  has  suggested  itself  that  it  may  be  due  to  the  com- 
plexity of  the  molecule  —  one  dilution  law  applying  to  solu- 
tions containing  molecules  of  a  certain  complexity,  while  an- 
other would  apply  to  solutions  containing  molecules  of  a 
different  order  of  complexity.  Of  the  many  dilution  laws 
for  strong  electrolytes  only  two  will  be  considered,  viz.,  that 
of  Rudolphi  and  that  of  Van't  Hoff.  The  Rudolphi  formula  is 


(i  —  ct)VF 
Van't  Hoff's  is 


(i  —  afV 
Since  the  Ostwald  law, 

a' 


=  K 
=  K 


(i  —  a)V 

applies  to  weakly  dissociated  electrolytes,  in  solutions  to  which 
it  applies  there  are  very  few  ions.  If  the  Rudolphi  formula 
is  applied  to  a  solution,  a  certain  volume,  Vlt  is  obtained, 
corresponding  to  a  definite  value  for  a  and  for  K.  If  now, 
retaining  the  same  values  as  before  for  a  and  for  K,  the  Ost- 
wald formula  is  applied  to  the  same  solution,  there  is  obtained 
a  volume  V  which  is  the  square  root  of  the  volume  obtained 
by  the  Rudolphi  formula.  In  other  words,  there  is  found 
the  relation  ^V1/V  =  i,  a  relation  which  would  indicate 
complexity  of  the  molecule  in  solutions  to  which  the  Rudolphi 
formula  applies.  Treating  the  Van't  Hoff  formula  in  the 
same  way,  i.  e.,  comparing  the  volume  obtained  by  the  use 
of  the  Van't  Hoff  formula  with  a  certain  solution,  for  a  definite 
value  of  a  and  of  K,  with  the  volume  obtained  by  the  use  of 
the  Ostwald  formula  for  the  same  solution,  keeping  a  and  K 
the  same  as  before,  there  is  found  the  relation 

V^        i  — a 

V^         a 

where  V  represents  the  volume  when  the  Ostwald  law  was 
applied  and  V1  the  volume  obtained  when  the  Van't  Hoff  law 
was  used.  Now  if  V/  V±  =  constant,  the  molecular  weight  would 
be  the  same  in  each  case ;  but  on  examining  the  formula  it  is 


12 

readily  seen  that  the  relation  is  not  a  constant  one,  but  that  it  is 
a  function  of  the  dissociation.  This  would  indicate  complexity 
of  the  molecule  in  solutions  to  which  the  van't  Hoff  law  applies. 
The  interesting  fact  about  this  last  relation  is  that  the  degree  of 
complexity  varies  with  the  dissociation,  i.  e.,  with  the  number  of 
ions  present;  just  exactly  what  has  been  referred  to  above  as 
the  probable  result  of  inductive  action.  Let  us  now  turn  to 
the  consideration  of  the  data  in  hand. 

EXPERIMENTAL 

The  well  known  Kohlrausch  method  was  used  to  deter- 
mine the  conductivities.  A  Kohlrausch  slide  wire  bridge 
was  employed  with  an  induction  coil  and  telephone  receiver. 
The  cells  used  were  of  the  type  designed  by  Jones  and  Bing- 
ham.1  The  cell  constants  were  redetermined  at  regular, 
short  intervals.  The  measurements  were  made  at  o°,  12°. 5, 
25°,  and  35°.  Three  separate  readings  were  taken  for  each 
solution  at  each  temperature,  different  resistances  being  used 
for  each  reading.  The  average  of  the  conductivities  obtained 
by  using  each  of  these  readings  was  taken  to  be  the  correct 
conductivity. 

The  flasks  and  burettes  were  carefully  calibrated  at  20° 
by  the  method  of  Morse  and  Blalock.2 

Solutions 

Kahlbaum's  "chemically  pure"  materials  were  taken  as 
the  starting  point  in  almost  every  case.  These  were  purified, 
whenever  practicable,  by  crystallization.  A  solution  some- 
what more  concentrated  than  the  most  concentrated  solution 
to  be  used  was  made  up.  Its  strength  was  determined  by 
volumetric  or  gravimetric  methods,  and  the  solutions  pre- 
pared from  it  as  a  mother  solution.  This  solution  was  made 
by  direct  weighing  whenever  it  was  possible,  and  in  the 
measurements  given  below  this  method  was  always  used  un- 
less otherwise  stated. 

Water 

The  water  used  in  making  the  solutions  was  prepared  ac- 

1  Am.  Chem.  J.,  34,  493  (1903). 

2  Ibid.,  16,  479  (1894). 


cording  to  the  method  of  Jones  and  Mackay,1  which  has  been 
employed  in  this  laboratory  for  many  years.  This  method  is 
too  well  known  to  need  discussion  here.  The  water  thus  ob- 
tained had  a  conductivity  of  about  0.9  to  1.3  X  io~6  at  o°. 
Discussion  of  Results 

The  following  salts  have  been  classified,  approximately, 
according  to  the  position  of  the  metal  in  the  Periodic  System. 
The  ammonium,  sodium  and  potassium  compounds  would, 
therefore,  be  first  in  order.  These  are,  therefore,  grouped  to- 
gether for  consideration.  A  careful  examination  of  the  re- 
sults for  these  compounds  will  show  some  points  of  interest. 

(i)  The  difference  in  the  conductivities  of  the  binary, 
ternary  and  quaternary  salts  is  quite  evident.  The  conduc- 
tivity of  ammonium  nitrate,  potassium  acetate,  and  potas- 
sium permanganate,  between  o°  and  35°,  ranges  from  46  at 
o°,  in  the  most  concentrated  solution  of  potassium  acetate, 
to  163.62  at  35°  in  the  most  dilute  solution  of  ammonium 
nitrate.  The  conductivity  of  those  compounds  which  are 
not  binary,  viz.,  ammonium  sulphate,  acid  ammonium  sul- 
phate, dipotassium  phosphate,  sodium  sulphate,  and  borax, 
at  35°  in  the  most  dilute  solutions  is,  in  every  case,  above 
200,  and  for  acid  ammonium  sulphate  is  considerably  above 
500. 

The  very  high  values  for  the  temperature  coefficients  of 
conductivity,  expressed  in  conductivity  units,  in  the  case  of 
the  four  sulphates  is  very  noticeable.  The  highest  values 
are  5,  6,  and  7+  in  the  case  of  sodium  sulphate,  ammonium 
sulphate  and  acid  ammonium  sulphate,  respectively;  while 
for  the  other  salts  under  consideration  in  this  group,  the 
temperature  coefficient  in  conductivity  units  is  4  +  .  This 
is  probably  due  to  the  fact  that  sulphates  show  a  tendency 
towards  polymerization. 

The  very  largest  temperature  coefficient  of  conductivity 
of  this  group  belongs  to  acid  ammonium  sulphate.  It  is 
7.96.  This  is  doubtless  accounted  for  by  the  fact  that  this 
salt  breaks  up  into  very  complex  ions. 

In  the  case  of  potassium  acetate  and  potassium  perman- 

1  Am.  Chem.  J.,  19,  91  (1897). 


ganate,  it  is  somewhat  peculiar  that  the  temperature  coeffi- 
cients of  conductivity  in  per  cent,  are  in  both  cases,  from  o° 
through  25  °,  larger  than  those  measured  in  conductivity  units. 

It  is  also  striking  that  in  the  case  of  acid  ammonium  sul- 
phate the  temperature  coefficients  of  conductivity  decrease 
with  rise  in  temperature. 

In  dealing  with  the  following  data  the  percentage  dissocia- 
tion is  not  discussed  for  the  individual  salts,  but  by  means  of 
curves  which  are  given  after  the  data  their  points  of  differ- 
ence are  brought  out. 

Ammonium  Nitrate 
Table  I— Conductivity 


V 
2 

0° 

58.44 

12°.  5 
78.92 

25° 
101.51 

35° 
119.48 

8 

64-35 

84.25 

H3.38 

135.07 

32 

68.81 

94-30 

I23-I3 

H6.53 

128 

71.64 

98.45 

128.44 

152.92 

512 

73-63 

101.39 

132.64 

157.48 

1024 

74.69 

102.51 

134-43 

159-44 

2048 

75-25 

103-39 

134.79 

160.39 

4096 

76.37 

105.51 

137.87 

163.62 

Table  II — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35< 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

2 

I  .64 

2.8l 

1.81 

2  .29 

I.  80 

1.77 

8 

i-59 

2.47 

2-33 

2.77 

2.17 

I.9I 

32 

2.04 

2.97 

2.31 

2-45 

2-34 

1.90 

128 

2-15 

3.0° 

2  .40 

2-44 

2.45 

I.9I 

512 

2.22 

3.02 

2.50 

2.47 

2.48 

1.86 

1024 

2.23 

2-99 

2-55 

2-49 

2.50 

1.86 

2048 

2.25 

2-99 

2.52 

2-44 

2.56 

1.90 

4096 

2-33 

3.05 

2-59 

2.46 

2.58 

1.87 

Table  III — Percentage  Dissociation 

V  0°  12°. 5                        25°  35° 

2  76.5  74.8  73.6  73.0 

8  84.2  79.9  82.2  82.6 

32  90.1  89.4  89.3  90.0 

128  93.8  93.3  ,93.2  93.5 

512  96.4  96.1  96.2  96.3 

1024  97.8  97.2  97.5  97.5 

2048  98.5  98.0  97.8  98.0 

4096  loo. o  zoo. o  100.0  ioo.  o 


Ammonium  Sulphate 

Table  IV  —  Conductivity 

V 

0° 

12°.  5 

25° 

35° 

2 

82.37 

112  .09 

I45-09 

170.72 

8 

98.06 

136.28 

179-57 

213.19 

32 

115.27 

160.26 

210.98 

254-86 

128 

I30-95 

182.65 

241.38 

291  .69 

512 

139.69 

195-77 

259.21 

313.00 

1024 

143  .  84 

202.31 

267.62 

322.55 

2048 

150.62 

209  .  74 

275.96 

337-47 

4096 

150.44 

211-55 

280.82 

340.32 

Table  V — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35< 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

2 

2.38 

2.89 

2.64 

2.36 

2.56 

1.76 

8 

3.06 

3.12 

3-46 

2-54 

3.36 

1.87 

32 

3.60 

3.12 

4.06 

2-53 

4-39 

2.08 

128 

4.14 

3-16 

4.70 

2-57 

5-03 

2.08 

512 

4-49 

3.21 

5.08 

2.60 

5.38 

2.08 

1024 

4.68 

3-25 

5.22 

2.58 

5-49 

2.05 

2048 

4-73 

3-H 

5-30 

2-53 

6.15 

2.23 

4096 

4.89 

3-25 

5-54 

2.58 

5-95 

2.  12. 

Table  VI — Percentage  Dissociation 

0°  12°. 5  25°  35' 

54.6         52.9         51.6         50.1 


8 

65.0 

64.4 

63-9 

62.6 

32 

76.5 

75-7 

75-i 

74-8 

128 

86.9 

86.3 

85-9 

85-7 

512 

92.7 

92.5 

92.3 

91.9 

1024 

95-4 

95-6 

95-2 

94-7 

2048 

100.  0 

99.1 

98.2 

99.1 

4096  99.8  ioo.  o  loo.  o  ioo.  o 

Acid  Ammonium  Sulphate 

Table  VII— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

2 

155.26 

186.49 

2  i  i  .  99 

226.O6 

8 

183.40 

223.84 

258.00 

277.18 

32 

223.58 

279-55 

322.68 

349-24 

128 

265.24 

339.00 

404.14 

444.74 

512 

289.79 

378.25 

463  .  20 

522.24 

1024 

295.22 

386.88 

483.5I 

547-05 

2048 

303.41 

4OO.OI 

496.86 

573.46 

4096 

304-26 

401  .  96 

497.11 

576.66 

i6 


Table  VIII — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units. 

cent. 

2 

2.50 

1.61 

2.04 

1.09 

I.4I 

0.66 

8 

4.04 

2.20 

2-73 

I  .22 

I.9I 

0.74 

32 

4-48 

2.OO 

3-45 

1.23 

2.66 

0.82 

128 

5.90 

2  .22 

5-21 

i-54 

4.06 

i  .01 

512 

7-08 

2.44 

6.79 

1.  80 

5-90 

1.27 

1024 

7-33 

2.48 

7-73 

2.00 

6-35 

i-3i 

2048 

7-73 

2-55 

7-74 

1.94 

7.66 

i-54 

4096 

7.81 

2-57 

7.61 

1.89 

7.96 

i  .60 

Table  IX — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

2  51.0  46.4  42.7  39.2 

8 

32 
128 
512 

1024 
2048 
4096  ioo. o  ioo. o  loo. o  loo.  o 

Sodium  Sulphate 
Table  X — Conductivity 

V  0°  12°. 5  25°  35° 


60.3 

55-7 

5i-9 

48.1 

73-5 

69.6 

65.0 

60.6 

87.1 

84.4 

81.3 

77.1 

95-2 

94.2 

93-2 

90.5 

97.0 

96.3 

97-4 

94-9 

99-7 

99  6 

99-9 

99-4 

4 

68.49 

97-54 

129.13 

156.71 

8 

78.51 

i  i  i  .  46 

146.40 

178.24 

32 

94-51 

132.72 

176.76 

215.19 

128 

107-54 

152.49 

203  .  10 

247.02 

512 

117.46 

166.24 

221  .21 

269.50 

1024 

119.65 

169.61 

226.34 

276.92 

2048 

125-95 

176.08 

235-35 

287.02 

4096 

127.73 

181.61 

243.42 

294.48 

Table  XI — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-3S9 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

2.32 

3-39 

2-53 

2-59 

2.76 

2.14 

8 

2.63 

3-35 

2.80 

2-51 

3-i8 

2.17 

32 

3-05 

3-23 

3-52 

2.65 

3-84 

2.17 

128 

3.59 

3-34 

4-05 

2.66 

4-39 

2.16 

512 

3-90 

3-32 

4.40 

2.65 

4-83 

2.18 

1024 

4-00 

3-34 

4-54 

2.68 

5.06 

2.19 

2048 

4-OI 

3-i8 

4-74 

2.69 

5-17 

2.20 

4096 

4-31 

3-37 

4-94 

2.72 

5-n 

2.10 

17 
Table  XII — Percentage  Dissociation 

V                           0°                        12°. 5                       25°  35° 

4               53-6             53-7             53- i  53-2 

8                61.4             61.4             60. i  60.5 

32               73-9             73-i             72.6  73.0 

128               84.1             84.0             83.4  83.9 

512               91.9             91.6             90.9  91.5 

1024               93.6             93.4             93.0  94.0 

2048               98.5             97.0             96.7  97.4 

4096             100.0           100.0           100.0  loo.o 

Borax 
Table  XIII— Conductivity 

V                  0°                      12°. 5                      25°  35° 

16    57-99     83.76    113-54  139-83 

32    64.36     92.74    125.49  154-61 

128    72.87    104.81    141.72  174-52 

512      78.04      112.22      152.00  187.97 

1024      79.20      II3-29      153-4°  189.37 

2048      83.45      119-55      I6I.23  198.31 

4096      85.50      122.28      163.99  202:65 

Table  XIV — Temperature  Coefficients 

0°-12°.5                                 12°. 5-25°  25°-35° 


Cond.  Per  Cond.  Per  Cond.               Per 

V            units  cent.  units  cent.  units               cent. 

16   2.06  3.55  2.38  2.84  2.63    2.32 

32   2.27  3.53  2.62  2.83  2.91    2.32 

128   2.56  3.51  2.95  2.82  3.28    2.32 

512   2.73  3.50  3.18  2.83  3.60    2.37 

1024   2.73  3.45  3.21  2.83  3.60    2.35 

2048   2.89  3.46  3.33  2.79  3.71    2.30^ 

4096   2.94  3.44  3.34  2.73  3.87    2.36 

Table  XV — Percentage  Dissociation 

V  0°                       12°. 5  25°                          35° 

16  67.8  68.5  69.2             69.0 

32  75-3             75-8  76.5             76.3 

128  85.3  85.7  86.4             86.1 

512  91.3  91.8  92.7             92.7 

1024  92.7             92.6  93.5             93.4 

2048  97.6             97.8  98.3             97.8 

4096  100.0  100.0  loo.o           100.0 


i8 

Potassium  Acetate 
Table  XV I—Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

46-13 

62.62 

83-35 

99.88 

8 

48.60 

67.  II 

88.43 

105.87 

32 

53-09 

73-59 

97.29 

117.46 

128 

55-57 

77-43 

102.13 

123.03 

512 

57-17 

79.91 

I05.I6 

126.87 

1024 

58.33 

81.14 

106  .  84 

I29.O9 

2048 

59.24 

82.09 

108.43 

129.84 

4096 

59.06 

81.89 

108.65 

129.90 

Table  XVII — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35' 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

•32 

2.86 

1.66 

2.64 

1.65 

I.98 

8 

.48 

3-05 

1.71 

2-55 

i-74 

i  97 

32       -1 

.64 

3-09 

i  .90 

2.58 

2.02 

2.07 

128         3 

•75 

3-15 

1.98 

2-54 

2.09 

2.05 

512 

.82 

3-17 

2.02 

2-53 

2.17 

2.06 

1024 

-83 

3-14 

2.06 

2-54 

2.23 

2.09 

2048 

-83 

3  09 

2.  II 

2-57 

2.14 

i-97 

4096 

-83 

3.10 

2.14 

2.61 

2.13 

1.96 

Table  XVIII — Percentage  Dissociation 


V 

0° 

12°.  5 

25° 

35° 

4 

77-8 

76.3 

76.6 

76.9 

8 

82.0 

81.8 

81-3 

81.5 

32 

89.6 

89.7 

89-5 

90.4 

128 

93-7 

94  4 

93-9 

94-7 

512 

96.4 

97-4 

96.7 

97.6 

1024 

98.4 

98.9 

98.3 

99  3 

2048 

100.  0 

100.  0 

99-7 

99-9 

4096 

99  -6 

99-8 

100.  0 

100.  O 

Potassium  Permanganate 

The  strength  of  the  mother  solution  was  determined  volu- 
metrically  by  means  of  potassium  tetroxalate. 


19 
Table  XIX — Conductivity 


V 

0° 

12°.  5 

25° 

35° 

8 

59-34 

8o.i7 

104  .  36 

124.74 

32 

63-75 

87-13 

113.70 

136.05 

128 

66.76 

91-38 

119.31 

142.42 

512 

66.46 

91.14 

117.90 

141.49 

1024 

64.65 

89-05 

113-95 

137.09 

2048 

63.72 

86.  6i 

110.80 

133.02 

4096 

62.64 

87.94 

I  I  I  .  8O 

133-97 

Table  XX — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35' 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

8 

.67 

2.8l 

1.94 

2.42 

2.O4 

I.96 

32 

-87 

2-93 

2.13 

2-45 

2.24 

1.97 

128 

•97 

2-95 

2.23 

2.44 

2.31 

1.94 

512 

•97 

2.96 

2.14 

2-35 

2.36 

2.OO 

1024 

•95 

3.02 

1.99 

2.24 

2.31 

2.03 

2048 

•83 

2.87 

1.94 

2.24 

2.22 

2.0O 

4096       j 

>.O2 

3-23 

I.9I 

2.17 

2.22 

1.99 

Table  XXI — Percentage  Dissociation 


V 

8 

0° 

88.8 

12°.  5 
87.7 

25° 
87-5 

35° 

87.6 

32 

95-4 

95-3 

95-3 

95-5 

128 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

512 

99-5 

99-7 

98.8 

99-4 

1024 

96.8 

97-4 

95-5 

96.3 

2048 

95-4 

94-8 

92.9 

93-4 

4096 

93-8 

96.2 

93-7 

94.1 

Dipotassium  Phosphate 

This  salt  was  precipitated  by  magnesia  mixture  and  the 
phosphoric  acid  thus  determined. 

Table  XXII— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

2 

63.01 

86.82 

II3.04 

138.16 

8 

79.19 

109.25 

143-34 

174.91 

32 

91.69 

127.42 

l67.6l 

203  .  80 

128 

102.47 

H2.37 

188.10 

230.71 

512 

107.76 

150.85 

199.40 

239.84 

1024 

109.35 

152.23 

200.52 

242.65 

2048 

110.47 

I57.04 

206.13 

242.54 

4096 

107.  16 

I54-98 

2OI  .98 

250.78 

20 


Table 

XXIII  —  Temperature  Coefficients 

0°-12°.5 

12°.  5-25°                                25°-35° 

Cond. 

Per 

Cond. 

Per               Cond.               Per 

units 

cent. 

units 

cent.              units               cent. 

I.9I 

3-03 

2.  10 

2.42            2.51             2.22 

2.4O 

3-03 

2-73 

2.50            3.l6            2.21 

2.86 

3-05 

3.22 

2.53            3.62            2.16 

3-19 

3-n 

3-66 

2.57            4.26            2.27 

3-45 

3-20 

3.88 

2.57            4.04            2.03 

3-43 

3-14 

3-86 

2.54            4.21            2.10 

3-73 

3.38 

3-93 

2.50            3.64            1.77 

3-83 

3-57 

3-76 

2.43            4.88            2.42 

Table 

XXIV—  Percentage 

Dissociation 

r 

0° 

12°.  5 

25°                        35° 

57-o 

55-3 

54-8             55-i 

7i-7 

69.6 

69.5             69.8 

83.0 

81.1 

81.3             81.3 

92.8 

90.7 

91.3             92.0 

97.6 

96.1 

96  •  7             95-7 

99.0 

96.9 

97-3             96.8 

IOO.O 

IOO.O 

loo.o            96.7 

97-0 

98.7 

98.0           100.0 

V 
2 
8 

32 
128 

512 
1024 
2048 

4096 


2 
8 

32 

128 

512 

1024 

2048 

4096 

The  group  consisting  of  strontium  acetate  and  magnesium 
bromide,  nitrate,  formate  and  acetate  will  be  considered  next. 

There  is  nothing  special  to  note  in  the  case  of  strontium 
acetate.  It  is  readily  hydrolyzed,  and  any  irregularities 
might  easily  be  attributed  to  this  fact.  Attention  might  be 
called,  however,  to  the  increase  in  percentage  dissociation 
with  rise  in  temperature. 

It  is  interesting  in  considering  the  data  of  the  four  mag- 
nesium compounds  to  discover,  if  possible,  the  effect  of  the 
different  anions.  Of  course,  the  water  of  crystallization 
would  also  be  a  factor.  This  is  the  same,  however,  in  the 
case  of  the  bromide  and  nitrate,  and  any  difference  in  the 
conductivity  of  these  two  compounds  may  correctly  be  attri- 
buted to  the  different  anions. 

On  examining  the  data  for  these  substances,  it  is  readily 
seen  that  the  conductivity  of  magnesium  bromide  is  decidedly 
greater  than  that  of  magnesium  nitrate.  Its  temperature 
coefficient  of  conductivity  is  also  larger.  This  would  point 


21 

to  some  difference  in  the  anions  either  as  to  velocity  or  com- 
plexity. Apart  from  their  remarkable  similarity,  magnesium 
acetate  and  formate  present  nothing  of  special  interest. 

Strontium  Acetate 

The  strontium  was  precipitated  and  weighed  as  the  car- 
bonate. 

Table  XXV— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

2 

34-94 

49.26 

66.52 

81.11 

8 

56.51 

80.19 

106  .  96 

129.99 

32 

70.69 

100.20 

135-25 

164.88 

128 

81.89 

II7.I9 

I57-69 

193-44 

512 

88.50 

128.09 

170.  16 

209.22 

1024 

91.18 

131.09 

177-44 

218.24 

2048 

97-30 

139.01 

180.07 

219.77 

4096 

97.89 

139.60 

184.44 

224.75 

Table  XXVI — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

2 

I-I5 

3-29 

1-38 

2.80 

I  .46 

2.  2O 

8 

1.89 

3-35 

2.14 

2.67 

2.30 

2-15 

32 

2.36 

3-34 

2.80 

2.79 

2.96 

2.  19 

128 

2.82 

3-44 

3-24 

2.77 

3-58 

2.27 

512 

3-17 

3-58 

3-37 

2.63 

3-91 

2.30 

1024 

3-19 

3-50 

3-70 

2.82 

4.08 

2.30 

2048          3.34  3.43  3.28  2.36  3.97  2.21 

4096       3-34         3-4i         3-59         2.57         4.03         2.19 


Table  XXVII — Percentage  Dissociation 

0°  12°. 5  25°  35' 


2 

35-7 

35-3 

36.1 

36.1 

8 

57-7 

57-4 

58-0 

57-8 

32 

72.2 

71.8 

73-4 

73-4 

128 

83-6 

83-9 

85-5 

86.1 

512 

90.4 

91.7 

92.3 

93-1 

1024 

93-i 

93-9 

96.4 

97.1 

2048 

99  3 

99.6 

97-7 

97-8 

4096  100.0          100.0          ioo. o          ioo.  o 


22 

Magnesium  Bromide 

The  magnesium  was  prcipitated  as  ammonium  magnesium 
phosphate,  and  weighed  as  the  pyrophosphate. 

Table  XXV 1 1  I—Conductivity 

V  0°  12°. 5  25°  35° 

2  76.34  104.05  132.92  162.25 

8    93-73    130.12    170.64    206.18 

32  104.56  147-24  194-42  235.51 

128  113.52  159-94  211.91  257.31 

512  118.93  167.72  223.06  270.40 

1024  122.80  173-39  230.94  279.38 

2048  127.28  179.74  238.70  289.52 

4096  130.91  185.06  244.94  305-94 

Table  XXIX— Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond.  Per  Cond.  Per  Cond.  Per 

V  units  cent.  units  cent.  units  cent. 

2  2.22  2.91  2.31  2.22  2.93  2 . 2O 

8  2.91  3.11  3.24  2.49  3.55  2.08 

32  3.41  3.26  3.77  2.56  4-II  2. II 

128  3.71  3.27  4.16  2.60  4.54  2.14 

512  3.90  3.28  4.43  2.64  4.73  2.12 

1024  4.05  3.30  4.60  2.65  4.84  2.10 

2048  4.20  3.30  4.72  2.63  5.08  2.13 

4096  4-33  3-31  4-79  2.59  6.10  2.49 


Table  XXX — Percentage  Dissociation 

V                          0°                       12°. 5                      25C  35° 

2                     58.3                  56.2                 54.3  53.0 

8               71.6             70.3             69.7  67.4 

32           79.9         79.5         79.4  76.9 

128               86.8            86.4            86.5  84.1 

512               90.9            90.6            91.1  88.3 

1024               93.9            93.7            94.3  91.3 

2048               97.3             97.1             97.5  94.6 

4096             100.0          100.0          100.0  loo.o 

Magnesium  Nitrate 
> 
The  magnesium  was  weighed  as  the  pyrophosphate. 


Table 

XXXII—  Temperature  Coefficients 

0°-12°.5 

12°.  5-25° 

25°-35° 

Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

units 

cent. 

units 

cent. 

units 

cent. 

2.76 

3.10 

2.99 

2.42 

3.10 

i-93 

3-23 

3-18 

3-61 

2-54 

3-61 

i-93 

3-58 

3-23 

3-54 

2.28 

4.29 

2.  10 

3-74 

3-14 

4.41 

2.66 

4-44 

2.OI 

3-97 

3-28 

4-34 

2-55 

4.78 

2.12 

3-99 

3-23 

4-52 

2.61 

5-04 

2.  II 

4.06 

3-30 

4-47 

2.57 

4.80 

2.09 

23 

Table  XXXI— Conductivity 

V        0°          12°. 5  25°           35° 

8    88.91    123.42  160.86  191.88 

32   101.55    14* -97  187.10  223.24 

128   110.78    155-50  204.72  247.66 

512   119.01   165.77  220.89  265.33 

1024   120.68    170.27  224.49  272.30 

2048   123.34    173-18  229.70  280.09 

4096   122.89    I73-70  229.58  277.54 


8 

32 

128 

512 

1024 

2048 

4096 

Table  XXXIII — Percentage  Dissociation 

V  0°  12°. 5  25°                        35° 

8  72.1  71.1  70.0             68.5 

32  82.4  81.7  81.5         79.7 

128  89.9  89.5  89.1           88.4 

512  96.5  95.4  96.2         94.7 

1024  97.9  98.0  99.7          97.2 

2048  100.0  99.7  100.0           loo.  o 

4096  99.7  ioo. o  99  96           99.1 

Magnesium  Formate 

The  magnesium  was  weighed  as  the  pyrophosphate. 
Table  XXXIV— Conductivity 

V  0°  12°. 5  25°                         35° 

2  37-33  52.53  69.24           83.25 

8  58.15  83.44  109.29         132-14 

32  74.68  106.05  141-71   172.3! 

128  85.99  122.17  164.06    200.30 

512  88.58  123.84  167.86    205.44 

1024  94.03  133-87  176.23   209.90 

2048  97.22  138.60  184.73    226.37 

4096  97.18  138.74  182.91    223.19 


24 

Table  XXXV— Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35( 


Cond.                Per  Cond.  Per               Cond.                Per 

V          units                cent.  units  cent.                units                cent. 

2     1.22      3.27  1.33  2.53      1.40     2.02 

8     2.02      3.47  2.07  2.48      2.29     2.10 

32     2.51      3.36  2.85  2.69     3.06      2.16 

128     2.89     3.36  3.35  2.74     3.62      2.21 

512     2.82      3.18  3.52  2.84     3.76      2.24 

1024     3.19     3.39  3.38  2.52      3.37      1.91 

2048   3.31    3.40  3.69  2.66    4.16    2.25 

4096    3.32     3.42  3.53  2.54     4.03     2.20 

Table  XXXVI — Percentage  Dissociation 

V                            0°  12°. 5  25°                          35° 

2               38-4  37-9  37-5             36.8 

8                59.8  60. i  59.2             58.4 

32                76.8  76.4  76.7             76.1 

128               88.4  88.1  88.8             88.5 

512                91.1  89.3  90.9             90.7 

1024               96.7  96.5  95.4             92.7 

2048               99.9  99-9  100.0           100.0 

4096             100.0  loo.o        99.05  98.6 

Magnesium  Acetate 

The  magnesium  was  determined  as  in  the  preceding  salt. 
Table  XXXVII— Conductivity 

V                   0°  12°. 5  25°                         35° 

4         37-56  54-50  72.50           88.92 

8         46.35  66.76  89.79         109.86 

32         60.99  87.97  119.31         146.20 

128         71.13  103.35  I39-5I         172.35 

512         78.05  113-23  I53-4I         189-50 

1024         80.38  116.73  158.95         201.71 

2048         83.85  121.36  164.72         203.07 

4096         84.99  121.76  165.38         203.70 

Table  XXXVIII — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 

Cond.               Per  Cond.  Per                 Cond.              Per 

V          units               cent.  units  cent.                units               cent. 

4   1.36    3.62  i-44  2.64    1.64    2.26 

8   1.63    3.52  1.84  2.76    2.01    2.24 

32   2.16    3.54  2.51  2.85    2.69    2.25 

128   2.58    3.63  2.89  2.80    3.28    2.35 

512    2. Si     3.60  3.21  2.83     3.61     2.35 

1024   2.91    3.62  3.38  2.89    4.28    2.69 

2048   3.00    3.58  3.47  2.86    3.84    2.33 

4096   2.94    3.46  3.49  2.87    3.83    2.32 


44-2 

44.8 

43-8 

43-7 

54-6 

54-8 

54-3 

53-9 

71.8 

72.2 

72.1 

71.8 

83.7 

84.9 

84-3 

84.6 

91.9 

93-0 

92.8 

93-0 

94.6 

95-9 

96.  i 

99.0 

98.7 

99-7 

99.6 

99-7 

Table  XXXIX— Percentage  Dissociation 

V  0°  12°. 5  25°  35' 

4 
8 

32 

128 

512 
1024 
2048 
4096  100. o  ioo. o  ioo. o  ioo. o 

The  next  group  taken  up  for  study  consists  of  cadmium 
chloride,  cadmium  bromide,  cadmium  iodide  and  lead  chlor- 
ide. Attention  should  be  called  to  the  fact  that  cadmium 
iodide,  having  no  water  of  crystallization,  has  just  about  the 
same  temperature  coefficients  of  conductivity  as  cadmium 
bromide  and  cadmium  chloride,  both  of  which  have  water  of 
crystallization.  Apparent  increase  of  percentage  dissocia- 
tion with  rise  in  temperature  is  unusual,  and  is  quite  notice- 
able in  the  case  of  cadmium  iodide. 

Lead  chloride  has  no  water  of  crystallization  but,  like 
cadmium  iodide,  has  high  temperature  coefficients  of  conduc- 
tivity. There  must  be  some  factor  operative  here  affecting 
temperature  coefficients  just  as  hydration  does,  but  which, 
from  the  nature  of  the  case,  cannot  be  due  to  hydrates. 

Cadmium  Chloride 

Silver  nitrate  was  used  to  precipitate  the  halogen  in  cad- 
mium chloride,  bromide  and  iodide. 

Table  XL — Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

33-65 

46.21 

60.15 

71.92 

8 

45-32 

60.85 

79-30 

94-59 

32 

65-63 

90-33 

II8-55 

142.48 

128 

88.34 

122.98 

162.32 

I95-7I 

512 

106.  14 

148.36 

197-57 

236.99 

1024 

113.78 

I59-65 

212-53 

258.73 

2048 

121  .  19 

166.23 

221.36 

269.00 

4096 

121.03 

172.78 

232.06 

282.43 

26 


Table  XLI — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per               Cond.               Per 

V          units 

cent. 

units 

cent.              units              cent. 

4  £  I-°° 

2.97 

I  .  12 

2.42         1.18         1.96 

8        1.24 

2.74 

1.47 

2.42             1.53             1.93 

32        1-97 

3-oi 

2.26 

2.50            2.39            2.02 

128,3     2.77 

3-14 

3-15 

2-54         3-34         2.06 

512       3.38 

3.18 

3-94 

2.66         3.94         1.99 

1024       3.67 

3.23 

4-23 

2.65         4.62         2.17 

2048       3  .  60 

2.97 

4.41 

2  .  65            4  .  76            2.10 

4096       4.14 

3-42 

4-74 

2.62            5.04            2.12 

Table 

XLII  —  Percentage 

Dissociation 

v 

0° 

12°.  5 

25°                       35° 

4 

27.8 

26.7 

25.9         25.5 

8 

37-4 

35-2 

34-2             33-5 

32 

54-2 

52.3 

5i-i             50-5 

128 

72.9 

71.2 

69.9             69.3 

512 

87.6 

85-9 

85-1             83.9 

1024 

93  9 

92.4 

91.6             91.6 

2048             100.0 

96.2 

95-4             95-3 

4096 

99  9 

IOO.O 

IOO.O               IOO.O 

Cadmium  Bromide 
Table  XLI  1 1— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

28.63 

40-59 

53-40 

64.51 

8 

37-80 

53-36 

70.44 

84.81 

32 

57.78 

82.06 

109.34 

132.69 

128 

79-77 

H3-57 

I5I-23 

184.16 

512 

101.37 

I43-25 

190.52 

232.83 

1024 

110.69 

156.85 

208  .  48 

252.81 

2048 

121.23 

170.89 

227.41 

275.22 

4096 

123.76 

I74-05 

232.20 

280.84 

Table  XLI V— Temperature  Coefficients 


0°-12°.5 


12°. 5-25° 


25°-35< 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

0.96 

3-35 

I  .02 

2.51 

I  .  II 

2.07 

8 

1.24 

3-28 

i-37 

2.56 

i-44 

2.03 

32 

1.94 

3-35 

2.18 

2.66 

2.34 

2.14 

128 

2.70 

3-38 

3-01 

2.65 

3-29 

2.18 

512 

3-55 

3-30 

3-78 

2.64 

4-23 

2.22 

1024 

3-69 

3-33 

4-13 

2.62 

4-43 

2.  12 

2048 

3-97 

3.21 

4-52 

2.64 

4.78 

2.  10 

4096 

4.02 

3-25 

4-65 

2.67 

4.86 

2.79 

27 

Table  XLV — Percentage  Dissociation 


V 

0° 

12°.  5 

25° 

35° 

4 

23.1 

23-3 

23.0 

23.0 

8 

30-5 

30.6 

30-3 

30.2 

32 

46.7 

47.1 

47.1 

47-3 

128 

64.4 

65.2 

65.I 

65-6 

512 

81.9 

82.3 

82.1 

82.9 

1024 

89.4 

9O.  I 

89.8 

90.0 

2048 

97  9 

98.2 

97-9 

98.0 

4096  100.0  ioo. o  ioo. o  ioo.  o 

Cadmium  Iodide 
Table  XLV  I— Conductivity 


V 

4 

0° 

20.45 

12°.  5 
29.76 

25° 
39-84 

35° 
48.41 

8 

24-31 

35-85 

48.44 

59-43 

32 

39-45 

59-23 

81-53 

101  .22 

128 

62.73 

93-36 

127.36 

157-35 

512 

87.06 

127.74 

172.93 

2  1  1  .  90 

1024 

96.31 

140.03 

188.66 

231.10 

2048 

109.01 

157.20 

209.73 

256.42 

4096 

118.78 

I7O.69 

224.93 

271.27 

Table  XLV  1 1 — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35( 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

0-75 

3-67 

0.8l 

2.72 

0.86 

2.16 

8 

0.92 

3.78 

I  .01 

2.82 

I.IO 

2.27 

32 

1.58 

4-01 

I.78 

3-01 

1.97 

2.42 

128 

2-45 

3-90 

2.72 

2.91 

3.00 

2.36 

512 

3-25 

3-73 

3-62 

2.83 

3-90 

2.26 

1024 

3-57 

3.7i 

3-82 

3-7i 

4.24 

2.25 

2048 

3-86 

3-54 

4-20 

3-67 

4.67 

'2.23 

4096      4.15       3.49       4.34       2.54       4.63       2.06 

Table  XLV  HI — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 


4 

17.2 

17.4 

17.7 

17.8 

8 

20.5 

21  .O 

21-5 

21.9 

32 

33-2 

34-7 

36.3 

37-3 

128 

52.8 

54-7 

56.6 

58.0 

512 

73-3 

74-8 

76.9 

78.1 

1024 

81.0 

82.6 

83-9 

85-2 

2048 

91.7 

92.1 

93-3 

94.5 

4096  100.0  100.0  100.0  IOO.O 


28 

Lead  Chloride 

The  lead  was  precipitated  by  means  of  sulphuric  acid  and 
weighed  as  lead  sulphate. 

Table  XLIX— Conductivity 

V  0°  12°. 5  25°  35° 


64 

104.41 

144.76 

188.71 

224.76 

128 

116.27 

161.56 

211.43 

252.17 

512 

133-10 

186.16 

246.31 

293-05 

1024 

136.89 

191.98 

253-96 

306.43 

2048 

138.88 

195.16 

258.49 

312.13 

4096 

144.70 

204  .  36 

270.26 

327.80 

Table  L — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35< 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

64 

3-23 

3-09 

3-52 

2-43 

3-61 

I.9I 

128 

3-63 

3.12 

3-99 

2.47 

4.07 

i-93 

512 

4-25 

3-19 

4.81 

2.58 

4.67 

1.90 

1024 

4.41 

3-22 

4.96 

2.58 

5-25 

2.07 

2048 

4-50 

3-24 

5-07 

2.60 

5-36 

2.07 

4096 

4-77 

3-30 

5-27 

2.58 

5-75 

2.13 

Table  LI — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

64  72.2  '70.8  69.8  68.6 

128  80.4  79.0  78.2  76.9 

512  92  .o  91 .  i  91 .  i  89.4 

1024  94.6  93.9  94.0  93.5 

2048  96.0  95.5  95.6  95.2 

4096  100.0  100.0  100.0  100.0 

The  aluminium  and  chromium  compounds  will  be  taken  up 
next  for  discussion.  In  these  compounds  we  should  expect 
to  find  strong  resemblances.  These  are  very  apparent. 
Chromium  and  aluminium  compounds,  with  respect  to  their 
conductivities,  are  in  a  class  by  themselves.  Their  very 
large  conductivities  and  their  exceedingly  large  temperature 
coefficients  must  attract  attention.  Their  very  large  conduc- 
tivities are  due  mainly  to  the  great  number  of  ions  into  which 
they  are  capable  of  ionizing  and  to  hydrolysis.  Judging  from 


29 


their  water  of  crystallization  and  from  freezing  point  lowerings,1 
they  must  be  hydra  ted  to  an  enormous  extent.  Their  large  tem- 
perature coefficients  of  conductivity  would  also  indicate  this  to  be 
the  fact.  The  change  in  conductivity,  both  with  rise  in  tempera- 
ture and  with  dilution,  is  much  more  gradual  in  the  case  of 
the  aluminium  salts  than  with  those  of  chromium.  The  ex- 
tremely small  percentage  dissociation  in  concentrated  solu- 
tions, in  the  case  of  chromium  sulphate  and  aluminium  sul- 
phate, is  worthy  of  notice.  This  is  probably  connected  with 
the  fact  that  sulphates,  especially  in  concentrated  solution, 
undergo  marked  polymerization. 

Aluminium  Chloride 

The  aluminium  was  determined  by  precipitating  the  hy- 
droxide and  weighing  as  the  oxide  A12O3.  This  was  done 
also  in  the  case  of  aluminium  nitrate  and  aluminium  sulphate. 


Table  LI  I — Conductivity 
o°  12°. s  25° 


35( 


4 

105.90 

147.40 

I93-5I 

232.54 

8 

120.22 

168.23 

220.86 

266.58 

32 

142.21 

20O  .  06 

265.12 

322.18 

128 

162.66 

231.08 

308  .  80 

377.28 

512 

176.77 

252.75 

341-24 

421  .06 

1024 

184.58 

266.73 

360.56 

446.95 

2048 

193-37 

279.49 

381.44 

472.46 

4096 

199.03 

290.06 

398.79 

499.92 

Table  LIII — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35< 


4 

8 

32 

128 

512 

1024 

2048 

4096 


Cond. 

Per 

units 

cent. 

3-32 

3-H 

3.84 

3-19 

4.63 

3-26 

5-47 

3-36 

6.08 

3-07 

6-57 

3-55 

6.89 

3-56 

7.28 

3-66 

Cond. 
units 


4.21 
5-2i 

6.22 
7.08 

7-51 
8.16 
8.70 


Per 
cent. 

2.50 
2.50 
2  .60 
2.69 
2.80 
2.82 
2  .92 
3.00 


Cond. 

Per 

units 

cent. 

3-90 

2.02 

4-57 

2.07 

5-7i 

2.15 

6.85 

2.22 

7-98 

2-34 

8.64 

2.40 

9.  10 

2-39 

IO.  II 

2-54 

i  Jones  and  Getman:  Am.  Chem.  J.,  31,  303  (1904).      Publication  No.  60,  Car- 
negie Institution  of  Washington. 


30 
Table  LIV — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

4  53.2  50.8  48.5  46.5 

8 

32 

128 

512 

1024 

2048 

4096  loo.o  100.0  100.0  loo.o 

Aluminium  Nitrate 
Table  LV — Conductivity 


60.4 

58.0 

55-4 

53-3 

71  .5 

69.0 

66.5 

64-4 

81.7 

79-7 

77-4 

75-5 

88.8 

87.1 

85-5 

84.2 

92.8 

91.9 

90.4 

89.4 

97-2 

96.3 

95-6 

94-5 

V 

0° 

12°.  5 

25° 

35° 

4 

102.82 

139.22 

180.52 

216.54 

8 

115.67 

158.84 

206  .  89 

248  .  82 

32 

136.32 

188.54 

247  -  70 

299.96 

128 

156.18 

217.14 

287.05 

349-49 

512 

166.97 

234-8I 

3I3-05 

384-43 

1024 

173-45 

247.08 

332.20 

410.18 

2048 

179.32 

255-68 

345-82 

428.32 

4096       187.89        272.12        372.07        462.84 
Table  LVI — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

2.91 

2.83 

3-30 

2-37 

3.60 

1.99 

8 

3-45 

2.98 

3-84 

2.42 

4.19 

2.03 

32 

4.18 

3-07 

4-75 

2-51 

5-23 

2.  II 

128 

4.88 

3.12 

5.60 

2.58 

6.25 

2.18 

512 

5-45 

3-25 

6.28 

2.67 

7.17 

2.28 

1024 

5-93 

3-40 

6.86 

2.77 

7.86 

2.36 

2048 

6.  19 

3-44 

7-31 

2.83 

8-37 

2-39 

4096 

6.90 

4-53 

8.19 

2-95 

9-32 

2-45 

Table  LVI  I — Percentage  Dissociation 

12°. 5  '    25°  35' 


4 

54-7 

51-2 

48.5 

46.8 

8 

61.6 

58.4 

55-6 

53-8 

32 

72.5 

69-3 

66.6 

64.9 

128 

83-1 

79-8 

77-i 

75-6 

512 

88.9 

86.3 

84.1 

83-1 

1024 

92-3 

90.8 

89-3 

88.7 

2048 

95-4 

94-0 

92.9 

92.6 

4096  loo.o  ioo. o  100.0  100.0 


Aluminium  Sulphate 
Table  LV II I— Conductivity 


V                0°                        12°.  5                      25°                      35° 

4         51.90           71-81           92.40         107.72 
8         65.21           89.81         114-44         i32-46 
32         89.50         123.63         158.01         183.51 
128        121.87         169.38         219.04         266.22 
512        164.08         230.86         301.01         358.79 
1024       191-95         271.31         359-i6         433-51 
2048       222.31         317-20         425-03         518.19 
4096       262.35         378.23         514-06         634.78 

Table  LIX  —  Temperature  Coefficients 

0°-12°.5                                12°.  5-25°                            25°-35° 

Cond. 

Per 

Cond. 

Per               Cond.               Per 

V         units 

cent. 

units 

cent.              units              cent. 

4       1-59 

3-06 

1.65 

2.30         1.53         1.66 

8        1-97 

3-02 

i  97 

2.19         i.  80         1.57 

32       2  .  73 

3-05 

2-75 

2.23         2.55         1.61 

128       3.80 

3.12 

3-97 

2.34         4.72         2.16 

512       5-34 

3.25 

5-6i 

2-43         5.78         1-79 

1024       6  .  34 

3-30 

7-03 

2.59         7.44         2.07 

2048       7  -  59 

3-41 

8.63 

2.72         9.32         2.19 

4096       9.27 

3-53 

10.87 

2.87       12.07         2.35 

Table  LX  —  Percentage 

Dissociation 

V 

0° 

12°.  5 

25°                       35° 

4 

19.8 

19.0 

18.0             17.0 

8 

24-9 

23-7 

22.3            20.9 

32 

34-i 

32.7 

30.7        28.9 

128 

46-5 

44-8 

42.6         41.9 

512 

62.5 

61.0 

58.5        56.5 

1024 

73-2 

71.7 

69.9          68.3 

2048 

84-7 

83-9 

82.7          81.6 

4096 

IOO.O 

IOO.O 

IOO.O              IOO.O 

Chromium  Chloride 

The  chromium  was  weighed  as  the  oxide  Cr2O3  in  the  case 
of  both  chromium  chloride  and  chromium  sulphate. 


32 
Table  LXI — Conductivity 


V 

0° 

12°.  5 

25° 

35°  . 

4 

86.30 

116.97 

I53-32 

199.  10 

8 

104.53 

138.83 

184.18 

243-55 

32 

130.03 

182.75 

245-00 

319.15 

128 

162.34 

231.28 

3I3-45 

393.62 

512 

188.46 

272.50 

372.34 

465  .  10 

1024 

200  .  2  I 

294-55 

403-58 

504.31 

2048 

214.48 

3I6.6O 

434-36 

543-02 

4096 

229.73 

34I-I4 

467.61 

580.16 

Table  LXII — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units. 

cent. 

4 

2-45 

2.84 

2.91 

2.49 

4.58 

2.99 

8 

2.74 

2.62 

3-63 

2.62 

5-94 

3-23 

32 

4.22 

3-25 

4.98 

2-73 

7-42 

3-03 

128 

5-52 

3-40 

6-57 

2.84 

8.02 

2-55 

512 

6.72 

3-57 

7-99 

2.93 

9.28 

3-95 

1024 

7-54 

3-77 

8.72 

2.96 

10.07 

2.50 

2048 

8.18 

3-82 

9.42 

2.98 

10.87 

2.50 

4096 

8.91 

3-88 

10.  12 

2.97 

11.26 

2.41 

Table  LXIII — Percentage  Dissociation 


V 

0° 

12°.  5 

25° 

35° 

4 

37-6 

34-3 

32-8 

34-3 

8 

45-5 

40.7 

39-4 

42.0 

32 

56.6 

53-6 

52-4 

55-0 

128 

70.7 

67.8 

67.0 

67.9 

512 

82.1 

79-9 

79-6 

80.2 

IO24 

87-2 

86.4 

86.3 

86.9 

2048 

93-3 

92.9 

92.9 

93-6 

4096 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

Chromium  Sulphate 
Table  LX IV— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

58.14 

78.48 

99.64 

II6.4I 

8 

77-85 

103.64 

I30.I8 

I5LI7 

32 

120.59 

158.67 

197.34 

230.37 

128 

169.08 

225.60 

283.56 

338.67 

512 

215-36 

292.66 

376.23 

472.16 

1024 

240  .  48 

329-96 

459.83 

561.76 

2048 

293-38 

405.65 

534-55 

708.14 

4096 

3I3-39 

445  •  16 

598.46 

808.29 

33 


Table  LXV  —  Temperature  Coefficients 

0°-12 

°.5 

12° 

,5-25° 

25 

°-35° 

Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

units 

cent. 

units 

cent. 

units 

cent. 

1.63 

2.80 

I  .69 

2.15 

1.68 

1.69 

2.06 

2.65 

2.12 

2.05 

2.  10 

1.61 

3-05 

2-54 

2.46 

3-30 

1.67 

4-52 

2.67 

4.64 

2.06 

5-51 

1.94 

6.18 

2.87 

4.69 

I.  60 

9-59 

2.55 

7.16 

2.98 

10.39 

3-15 

IO.  IO 

2.22 

8.98 

3.06 

10.31 

2-54 

17.36 

3-25 

10.38 

3-29 

12.26 

2-75 

20.98 

3-51 

4 
8 

32 

128 

512 
1024 
2048 

4096 

Table  LXVI — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

4  18.4  17.6  16.6  14.4 

8  24.7  23.3  21.7  18.7 

32  38.2  35.6  33.0  28.5 

128  53.6  50.7  47.4  41.9 

512  68.3  65.7  62.8  58.5 

1024  76.2  74.1  76.8  69.5 

2048  93.0  91.1  89.3  87.7 

4096  100.0  ioo. o  loo. o  loo.  o 

In  the  next  group  will  be  considered  manganous  sulphate, 
silver  nitrate,  copper  sulphate  and  cobalt  bromide.  Man- 
ganous sulphate  calls  for  no  comment.  The  data  obtained 
for  silver  nitrate  are  remarkably  similar  to  those  obtained  for 
ammonium  nitrate.  It  apparently  behaves  as  any  other 
ordinary,  unhydrated,  binary  compound.  It  differs  from 
ammonium  nitrate  in  that  its  percentage  dissociation,  appar- 
ently decreasing  with  rise  in  temperature  from  o°  to  25°,  in- 
creases somewhat  at  35°. 

The  data  for  copper  sulphate  resemble  strikingly  those  ob- 
tained for  manganous  sulphate,  cadmium  bromide  and  cad- 
mium iodide.  At  ordinary  temperatures  manganous  sulphate 
and  copper  sulphate  have  the  same  amount  of  water  of  crys- 
tallization. That  their  temperature  coefficients  should  be 
approximately  the  same  is  not  surprising;  but  that  the  tem- 
perature coefficients  of  cadmium  chloride  and  cadmium  bro- 
mide, crystallizing  with  less  water,  and  cadmium  iodide, 
crystallizing  with  no  water,  should  be  the  same  is  surprising. 


34 

The  temperature  coefficients  of  conductivity  of  cobalt 
bromide  indicate  much  hydration,  as  would  be  expected  from 
its  water  of  crystallization. 

Manganous  Sulphate 

The  manganese  was  weighed  as  the  pyrophosphate. 
Table  LX  VI I— Conductivity 


V                  0°                       12°.  5                      25°                       35° 

4         37-25           5i-8o           67.17           79.11 
8         44.11          .61.37           79.77           94.06 

32             59.65                83.47             109.27             129.72 
128             79.46             IH-74             147.24             I76.IO 

512         97-99         138.76         184.58         222.69 
1024       107.12         152.31         202.94         245.72 
2048        116.15         165.28         221.33         268.33 
4096        124.47         177-56         238.20         289.39 

Table  LXVIII  —  Temperature  Coefficients 

0°-12°.5                               12°.  5-25°                             25°-35° 

Cond. 

Pa- 

Cond. 

Per              Cond.              Per 

V           units 

cent. 

units 

cent.              units             cent. 

4       1.16 

3-" 

1.23 

2.38            I.I9            1.77 

8       1.38 

3.13 

i-47 

2.40            1.43            1.79 

32       1.91 

3-20 

2.06 

2.47         2.05         1.88 

128       2.58 

3.25 

2.84 

2.54        2.89         1.96 

512       3.26 

3-33 

3-67 

2.64        3.81         2.06 

1024       3  .  62 

3-38 

4-05 

2.66         4.28         2.  i  i 

2048       3-93 

3.38 

4.48 

2.71            4.7O           2.12 

4096       4.25 

3.42 

4-85 

2.73            5.12            2.15 

Table 

LXIX—  Percentage 

Dissociation 

V 

0* 

12°.  5 

25°                      35* 

4 

29.9 

29.2 

28.2         27.3 

8 

35-4 

34.6 

33.5         32.5 

32 

47-9 

47.0 

45.9         44.8 

128 

63-8 

62.9 

61.8         60.8 

512 

78.7 

78.1 

77-5             76.9 

1024 

86.1 

85.8 

85.2             84.9 

2048 

93-3 

93-i 

92  .  9            92  .  7 

4096             100.  o 

100.  O 

IOO.O               IOO.O 

35 

Silver  Nitrate 

The  silver  was  weighed  as  the  chloride. 
Table  LXX — Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

51-43 

70.55 

91.63 

109.95 

8 

56.01 

76.68 

99.80 

120.37 

32 

61.80 

85.30 

III  .20 

I33.I4 

128 

65.79 

91  .06 

119.14 

142.67 

512 

69.24 

94-99 

125.23 

148.77 

2048 

69.83 

96.67 

I26.8I 

151.24 

4096 

71.03 

99-03 

129.68 

153.32 

Table  LXX  I— Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35' 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

L53 

2.98 

1.69 

2.40 

1.83 

2.OO 

8 

1.65 

2-95 

1.65 

2-15 

2.O6 

2.O6 

32 

1.88 

2-94 

2.07 

2.43 

2.19 

1.97 

128 

2.  02 

2-94 

2.25 

2.47 

2-35 

1.97 

512 

2.O6 

2.98 

2.42 

2-55 

2-35 

1.87 

2048 

2.15 

3.01 

2.41 

2-49 

2.44 

I  .92 

4096 

2.24 

3-15 

2-45 

2.47 

2.36 

1.82 

Table  LXXII — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

4  72.4  71-3  70.6  71.7 

8  78.8  77.4  76.9  78.5 

32  87.0  86.2  85.7  86.8 

128  92.6  92.0  91.8  93.1 

512  97.4  95.9  96.5  97.0 

2048  98.3  97.6  97.7  98.7 

4096  100. o  ioo. o  100.0  100.0 


Cobalt  Bromide 

This  salt  was  precipitated  by  means  of  silver  nitrate,  and 
the  bromine  determined  from  the  weight  of  silver  bromide 
obtained. 


Table  LXXI 1 1— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

87.82 

I2O.24 

I55-60 

196.30 

8 

95-04 

131.29 

171.30 

204  .  48 

32 

105  •  56 

147.10 

193.09 

233.04 

128 

115.88 

162.  19 

2I4.O2 

259.9I 

512 

119.47 

169.42 

224.49 

273-44 

1024 

120.80 

173.38 

23L56 

28l.l6 

2048 

124.00 

174.68 

234.28 

282.65 

4096 

125-45 

177.93 

236.78 

289.34 

Table  LXXIV  —  Temperature  Coefficients 

0°-12°.5 

12°.  5-25° 

25°-35° 

Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

4 

2-59 

2-95 

2.83 

2-35 

4.07 

2.62 

8 

2.90 

3-05 

3-20 

2.44 

3-32 

1.94 

32 

3-32 

3-15 

3.68 

2.50 

4-00 

2.07 

128 

3-71 

3-20 

4.15 

2.56 

4-59 

2.15 

512 

4.0O 

3-35 

4.41 

2.60 

4.90 

2.18 

1024 

4.21 

3-49 

4-65 

2.68 

4.96 

2.14 

2048 

4-05 

3-27 

4-77 

2.73 

4.84 

2.07 

4096 

4.20 

3-35 

4.71 

2.65 

5.26 

2.22 

Table  LXXV — Percentage  Dissociation 


V 

0° 

12°.  5 

25° 

35° 

4 

70.0 

67.6 

65.7 

67.8 

8 

75-7 

73-8 

72.3 

70.7 

32 

84.1 

82.7 

81.5 

80.5 

128 

92-3 

92  .0 

90.4 

89.8 

512 

95-2 

95-2 

94-8 

94-5 

1024 

96.3 

97-5 

97-8 

97-2 

2048 

98.8 

98.2 

98.9 

97-7 

4096 

100.  0 

100.  0 

IOO.O 

IOO.O 

Copper  Sulphate 

The  sulphuric  acid  in  this  salt  was  precipitated  and  weighed 
as  barium  sulphate. 


37 
Table  LX XV I— Conductivity 


V                   0°                       12°.  5                         25°                       35° 

2         3°-°6           42.12           55-1*           65  -r5 
8         42.30           59.35           77.33           91.16 

32       57-24        80.53       105.64      124.94 
128        76.91        108.74        143.21        170.60 
512         97.88         138.92         184.97        221.08 
1024      105.85        150.86       202.57        245.05 
2048       113.36         161.78        217.71         264.44 
4096      119.18        171.07        231.27        281.42 

Table  LX  XV  1  1—  Temperature  Coefficients 

0°-12°.5                            12°.  5-25°                                25°-35° 

Cond. 
units 

Per 

cent. 

Cond. 
units 

Per 

cent. 

Cond. 
units 

Per 

cent. 

0.96 

3   19 

I  .04 

2.47 

I  .00 

.82 

1.36 

3-22 

1.44 

2-43 

1.38 

•79 

1.86 

3-25 

2.01 

2.50 

i-93 

•83 

2-54 

3-30 

2.76 

2-54 

2.74 

.91 

3-28 

3-35 

3-68 

2.65 

3.61 

•95 

3.60 

3-40 

4.14 

2-74 

4-25 

2.  10 

3-87 

3  -41 

4-47 

2.76 

4.67 

2.15 

4-15 

3-48 

4.82 

2.82 

5.02 

2.17 

V 
2 

8 

32 

128 

512 

1024 

2048 

4096 

Table  LXXVIII — Percentage  Dissociation 

V  0°  12°. 5  25°  35° 

2  25.2  24.6  23.8  23.2 

8  35-5  34-7  33-4  32-4 

32  48.0  47.1  45.7  44.4 

128  64.5  63.6  61.9  60.6 

512  82.1  81.2  80.0  78.6 

1024  88.8  88.2  87.6  87.1 

2048  95.1  94.6  94.1  94.0 

4096  100. o  100. o  100. o  loo.o 

The  conductivity  values  obtained  for  uranyl  sulphate 
and  uranyl  acetate  do  not  agree  satisfactorily  with  those  ob- 
tained by  West.1  His  solutions  were  evidently  standardized 
on  a  different  basis.  It  should  be  noticed  that  the  tempera- 
ture coefficients,  in  conductivity  units,  of  uranyl  sulphate  de- 
crease with  rise  in  temperature  through  V  =  512.  After  this 
dilution  they  increase,  as  in  the  case  of  the  other  uranyl  salts. 
The  percentage  dissociation  of  uranyl  acetate  apparently 

1  Am.  Chem.  J.,  44,  537  (1910). 


38 

increases  with  rise  in  temperature  through  V  =  128.  The 
more  dilute  solutions  show  a  decrease  with  rise  in  tempera- 
ture. This  may  be  seen  in  the  curve  for  uranyl  acetate  which 
follows. 

Uranyl  Chloride 

The  uranium  in  uranyl  chloride,  nitrate,  sulphate  and  acetate 
was  precipitated  by  means  of  ammonium  hydroxide  and 
weighed  as  the  oxide  U3O8. 

Table  LX XIX— Conductivity 


V 

0° 

12°.  5 

25° 

35° 

4 

101.45 

139.09 

180.45 

214.70 

8 

110.48 

157.64 

206.01 

246.51 

32 

I33-05 

186.56 

246  .  I  2 

297.84 

128 

148.39 

209.75 

279.00 

339-40 

512 

I55'98 

22O.7O 

296.56 

360.44 

1024 

161  .02 

23I-37 

311.92 

383.88 

2048 

168.42 

242.69 

328.24 

405  -  98 

4096 

174.98 

254.22 

348.16 

433-68 

Table  LX XX— Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

[units 

cent. 

units 

cent. 

units 

cent. 

4 

3.01 

2-97 

3-31 

2.38 

3-43 

I  .90 

8 

3-77 

3-41 

3-87 

2.46 

4-05 

1.97 

32 

4.28 

3-22 

4.76 

2-55 

5-17 

2.  10 

128 

4.91 

3-31 

5-54 

2.64 

6.04 

2.17 

512 

5-i8 

3-32 

6.07 

2-75 

6-39 

2.16 

1024 

5.63 

3-50 

6-44 

2.78 

7.20 

2.31 

2048 

5-94 

3-53 

6.84 

2.82 

7-77 

2-37 

4096 

6-34 

3-62 

7-52 

2.96 

8-55 

2.46 

Table  LXXXI — Percentage  Dissociation 

0°  12°. 5  25°  35' 


32 
128 
512 

1024 
2048 

4096 


58.0 

54-7 

51-8 

49-5 

63.1 

62.0 

59-2 

56.8 

76.0 

73-4 

70-7 

68.7 

84.8 

82.5 

80.2 

78.2 

89.1 

86.8 

85-2 

83.1 

92.0 

91  .0 

89.6 

88.5 

96.3 

95-5 

94-3 

93-6 

100.  0 

100.  0 

IOO.O 

IOO.O 

39 

Uranyl  Nitrate 
Table  LX XXI I— Conductivity 

V                  0°                     12°. 5                         25°  35° 

4    74-91    102.01    132.91  158.84 

8    83.44    II4-7I    I50-57  181.20 

32    97.22    i36-35    180.64  219.38 

128   110.14    153-84    207.89  254.21 

512   116.33    166.65    224.95  277.35 

1024   123.14    I77-76    241.47  298.63 

2048   128.92    187.20    255.38  317-44 

4096     136.77     200.10     274.50  343-09 

Table  LXXXIII — Temperature  Coefficients 

0°-12°.5                               12°. 5-25°  25°-35° 


2.90 

2-47 

2.42 

2-59 

i-95 

3-oo 

3-07 

2.68 

3-o6 

2.03 

3-22 

3-54 

2.60 

3-87 

2.14 

3-32 

4.16 

2.67 

4-63 

2.23 

3-47 

4.66 

2.80 

5-24 

2.33 

3-55 

5-io 

2.87 

5-72 

2-37 

3-62 

5-46 

2.92 

6.21 

2-43 

3-7i 

5-95 

2-97 

6.86 

2.50 

Cond.              Per  Cond.  Per               Cond.                Per 

V           units               cent.  units  cent.              units               cent. 

4       2.17 
8       2.50 

32       3-13 

128       3.66 

512  4.03 
1024  4.37 
2048  4 . 66 
4096  5-07 

Table  LXXXIV — Percentage  Dissociation 

V                         0°  12°. 5  25°                       35° 

4               54.8  51.0  48.4             46.3 

8               61.0  57.3  54.9             52.8 

32               71.1  68.1  65.8             63.9 

128               80.5  77.9  75.8             74.1 

512               85.0  83.3  82.0             80.8 

1024               90.0  88.8  88.0             87.1 

2048               94.2  93.6  93.1             92.5 

4096             100. o  ioo. o  ioo. o           ioo. o 

Uranyl  Sulphate 
Table  LXXXV— Conductivity 

V                   0°  12°. 5  25°                        35° 

8    78.13  99-77  120.82    136-43 

32   100.65  129.52  156.80    176-52 

128   128.62  166.72  203.02    229.42 

512   157-54  207.90  257.69    295.20 

1024   175-68  235.28  296.95    343-01 

2048   191.68  260.77  332.57    391-00 

4096   203.33  285.05  373-65    446.33 


40 
Table  LXXXVI — Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

-—  N 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

8 

i-73 

2.22 

1.68 

1.68 

1.56 

.29 

32 

2.31 

2.30 

2.18 

1.68 

1.97 

.26 

128 

3-05 

2-37 

2.90 

i-74 

2.64 

•30 

512 

4-03 

2.56 

3.98 

1.91 

3-75 

.46 

1024 

4-77 

2.72 

4-93 

2.  10 

4.61 

•55 

2048 

5-53 

2.89 

5-74 

2.  2O 

5-84 

.76 

4096 

6-54 

3.22 

7.09 

2-49 

7.27 

•95 

Table  LXXXVI  I — Percentage  Dissociation 

V  0°  12°. 5  25°  35" 

8 

32 
128 
512 

1024 
2048 
4096  loo.o  ioo. o  loo.o  ioo. o 

Uranyl  Acetate 
Table  LX XXV 1 1 1— Conductivity 

V  0°  12°. 5  25°  35° 


38.4 

35-0 

32.3 

30.6 

49-5 

45-4 

42.0 

39  -6 

63-2 

58.5 

54-3 

51-4 

77-5 

72.9 

69.0 

66.2 

86.4 

82.5 

79-5 

76.9 

94.2 

9i-5 

89.0 

87.6 

8 

30-59 

42.75 

56.53 

68.12 

32 

39-65 

55-08 

72.25 

86.67 

128 

51-48 

70.66 

91-34 

108.52 

512 

63-57 

86.06 

110.47 

129.06 

1024 

70.13 

94-74 

120.37 

141  .  12 

2048 

76.81 

103.65 

131.78 

154.46 

4096 

83-75 

113.81 

145.10 

170.54 

Table  LXXXIX— Temperature  Coefficients 

0°-12°.5  12°. 5-25°  25°-35° 


Cond. 

Per 

Cond. 

Per 

Cond. 

Per 

V 

units 

cent. 

units 

cent. 

units 

cent. 

8 

0.97 

3.12 

I  .  10 

2-57 

1.16 

2-05 

32 

1.23 

3.10 

1-37 

2-49 

1.44 

1.99 

128 

i-53 

2.97 

1-65 

2-34 

1.72 

1.88 

512 

i.  80 

2.83 

i-95 

2.26 

1.86 

1.68 

1024 

1.97 

2.8l 

2.05 

2.16 

2.08 

i-73 

2048 

2-15 

2.80 

2.25 

2.17 

2.27 

1.72 

4096 

2.41 

2:88 

2.50 

2.20 

2-54 

1-75 

36.5 

37-6 

39-0 

40.0 

47-3 

48.4 

48.8 

50.8 

61.5 

62.1 

63.0 

63-7 

75-9 

75-6 

76.1 

75-7 

83-7 

83-3 

83-0 

82.8 

91.7 

91.1 

90.8 

90.6 

Table  XC — Percentage  Dissociation 

V  0°  12°. 5  25°  35* 

8 

32 

128 

512 

1024 

2048 

4096  ioo. o  loo. o  loo. o  TOO. o 

FIGURES 

So  far  little  or  nothing  has  been  said  in  regard  to  the  per- 
centage dissociation  of  the  salts  studied.  Attention  will  be 
called  to  these  by  means  of  curves.  The  curves  of  ten  of  the 
thirty  salts  showed  the  percentage  dissociation  to  be  almost 
a  linear  function  of  rise  in  temperature.  Plotting  percentage 
dissociation  as  ordinates  against  rise  in  temperature  as  ab- 
scissae, for  each  dilution,  in  ten  cases  out  of  the  thirty,  curves 
were  obtained  resembling  the  one  for  aluminium  sulphate, 
Fig.  I.  The  other  20  salts  all  showed  variations  in  the  maxima 
or  minima.  Some  of  these  are  very  slight.  Diagrams  of  the 
most  striking  variations  follow.  The  salts  giving  curves 
showing  the  percentage  dissociation  to  be  a  linear  function 
of  rise  in  temperature  were  acid  ammonium  sulphate,  alu- 
minium nitrate,  aluminium  chloride,  aluminium  sulphate, 
uranyl  chloride,  uranyl  sulphate,  uranyl  nitrate,  chromium 
sulphate,  cadmium  chloride  and  manganous  sulphate.  The 
others  showed  more  or  less  variations,  the  most  striking  being 
here  represented. 

Fig.  II  is  very  interesting,  showing  in  the  case  of  cadmium 
iodide  the  increase  in  percentage  dissociation  with  rise  of 
temperature  from  V  =  8  to  V  —  2048. 

From  the  curve,  Fig.  Ill,  it  is  easily  seen  that  the  percentage 
dissociation  of  chromium  chloride  increases  decidedly  with  rise 
in  temperature  between  25°  and  35°.  The  increase  becomes 
less  and  less  as  the  dilution  increases. 

Uranyl  acetate  shows  an  increase  in  percentage  dissociation 
in  the  more  concentrated  solutions,  but  at  greater  dilutions 
gives  a  falling  curve  (Fig.  IV) . 


8o 


60 


40 


30 


2048 


1024 


512 


128 


20 

I- 


10 


12.5  as 

Temperature 
Fig.  I — Aluminium  Sulphate 


35 


43 


2048 


1024 


512 


128 


12.5  25 

Temperature 
Fig.  II— Cadmium  Iodide 


-»     8 
35 


44 


2048 


1024 


512 


128 


12.5  25 

Temperature 
Fig.  Ill — Chromium  Chloride 


35 


45 


2048 


*      1024 


512 


JO   * 


12.5  25 

Temperature 
Fig.  IV— Uranyl  Acetate 


35 


700  «»- 


12.5  25 

Temperature 
Fig.  V— Silver  Nitrate 


ZOO' 


3  80 


70 


12.5  25 

Temperature 
Fi«.  VI— Magnesium  Nitrate 


47 

Silver  nitrate  shows  a  decided  increase  in  percentage  disso- 
ciation with  rise  in  temperature  from  V  —  4  to  V  =  2048. 
See  Fig.  V. 

The  curves  representing  magnesium  nitrate  and  magnesium 
bromide  (Figs.  VI  and  VII)  show  a  remarkable  resemblance. 
The  maxima  at  higher  dilutions  are  pronounced. 


80 


128 


12.5  25  3 

Temperature 

Fig.  VII — Magnesium  Bromide 

An  examination  of  the  curves  raised  the  question,  what  pro- 
duces this  variation?  The  apparent  increase  in  percentage 
dissociation  with  rise  in  temperature  would,  naturally,  be 
thought  to  be  due  to  hydration.  When  there  is  little  or  no 
hydration  the  question  becomes  more  difficult  to  answer.  If, 
however,  the  ions  are  assumed  to  be  complex,  rise  in  tem- 
perature would  bring  about  greater  dissociation,  and  the  effect 


48 

would  be  just  the  same  as  if  hydrates  had  been  present.  It  is 
difficult  to  differentiate  the  two  factors.  That  hydrates  exist  is 
not  doubted.  The  complexity  of  the  ions  is  not  so  well  estab- 
lished, so  that  we  shall  present  arguments  only  for  the  latter. 
If  the  change  were  a  gradual  increase,  it  might  be  attributed 
easily  to  hydration,  but  a  change  from  an  increase  to  a  de- 
crease in  dissociation  could  not  be  accounted  for  in  this  way; 
whereas  complex  ions  once  dissociated  might  reach  a  state 
where  recombination  would  take  place.  Moreover,  the  amount 
of  hydration  has  been  found  to  depend  on  the  amount  of  water 
of  crystallization.  In  several  of  the  preceding  salts,  notably 
in  the  case  of  cadmium  compounds,  cadmium  iodide,  which 
has  no  water  of  crystallization,  is  found  to  have  temperature 
coefficients  of  conductivity  equal  in  magnitude  to  those  of 
cadmium  chloride,  cadmium  bromide  and  copper  sulphate, 
all  of  which  have  water  of  crystallization.  Lead  chloride, 
also,  which  has  no  water  of  crystallization,  has  temperature 
coefficients  which  compare  well  with  those  of  substances 
that  are  much  hydrated,  i.  e.,  copper  sulphate  and  cobalt 
bromide.  This  would  indicate  that  there  must  be  some  other 
factor  present  producing  the  same  effect  as  hydration. 

SUMMARY 

1.  In  the  main  the  results  obtained  in  the  case  of  the  thirty 
salts  studied  tend  to  confirm  the  earlier  results. 

2.  Without  exception  conductivity  increases  with  rise  in 
temperature  and  with  dilution. 

3.  The  temperature  coefficients  of  conductivity  expressed 
in  conductivity  units,  with  two  exceptions,  increase  with  rise 
in  temperature,  while  the  temperature  coefficients  expressed 
in  percentage  decrease. 

4.  Salts  greatly  hydrated   have  large   temperature   coeffi- 
cients.   The  amount  of  hydration,  judged  by  the  tempera- 
ture coefficients,  seems  closely  related  to  the  water  of  crys- 
tallization. 

5.  The  apparent  exceptions  to  the  results  earlier  obtained, 
viz.,  an  increase  in  percentage  dissociation  with  rise  in  tem- 
perature and  a  large  temperature  coefficient  when  there  is  no 


49 

reason  to  expect  large  hydration,  point,  in  the  opinion  of  the 
author,  strongly  to  the  view  advanced  above,  that  inductive 
action  takes  place  through  the  solvent  between  charged  ions 
and  neutral  molecules,  and  that  this  gives  rise  to  complex 
molecules  and  ions  in  solution. 

After  sufficient  work  has  been  done  in  this  field,  it  is  hoped 
to  bring  together  all  of  the  conductivity  and  dissociation  data 
obtained  in  this  laboratory  and  to  publish  them  as  a  mono- 
graph. However,  before  this  is  done  it  is  intended  to  repeat 
the  work  with  every  substance,  where  the  repetition  is  not 
already  completed  starting  with  new  material,  repurifying, 
restandardizing  and  remeasuring  the  conductivity. 

Work  will  be  continued  in  this  laboratory  along  the  lines 
indicated  above,  probably  for  at  least  the  next  ten  years, 
and  there  will  be  six  investigators  working  here  in  this  field 
during  the  next  academic  year. 


BIOGRAPHY 

Lula  Gaines  Winston,  the  author  of  this  dissertation,  is  a 
daughter  of  Professor  Charles  H.  Winston,  LL.D.,  of  Rich- 
mond College,  Virginia.  Having  graduated  at  the  Richmond 
High  School,  she  entered  Richmond  College  and  received  the 
degree  of  B.S.  in  1899. 

Since  that  time  she  has  attended  the  Harvard  Summer 
School  for  three  years,  taking  courses  in  Chemistry  and 
Physics. 

During  the  session  1901-1902,  she  was  teacher  of  Science  in 
the  Richmond  Female  Seminary.  In  1902  she  was  elected 
teacher  of  Chemistry  and  Physics  in  the  State  Female  Normal 
School,  Farmville,  Virginia,  which  position  she  still  holds,  hav- 
ing been  given  leave  of  absence  for  the  past  two  years  to  pursue 
her  studies  at  Johns  Hopkins  University. 


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